Nonlinear model to calculate the stressed state of a center-wound roll

Abstract

This work develops a model to calculate the stressed state of center-wound rolled webs, such as film, paper, or foil. The model is built on a lesser known linear model developed by Umanskii and accounts for the nonlinear stress-strain relationship of the roll in the radial direction as determined from uniaxially compressing a stack of the material. The main cause of this nonlinear behavior is inter-layer air entrapment and web surface roughness. The more popular published linear model developed by Altmann has been extended by Hakiel to include the roll's nonlinear radial stress-strain relationship. However, recent published work shows the radial stresses predicted by Hakiel to be significantly greater than measured data using calibrated pull labs for some webs.

Results from this nonlinear model are compared to published measured in-roll radial stress data for three materials: PET, newsprint, and bond paper. After eliminating the softest portion of the stack test data, the model predicted in-roll radial stresses that agree well with the experimental data for PET. The predicted in-roll radial stresses were less than the experimental data for both papers. However, results from the Hakiel model and the new nonlinear model were found to provide bounds for the exerimental data for paper.